%0 Journal Article
%T An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles
%A M. Ibrahim Moussa
%J International Journal on Applications of Graph Theory in Wireless ad hoc Networks and Sensor Networks
%D 2010
%I Academy & Industry Research Collaboration Center (AIRCC)
%X In 1991, Gnanajothi [4] proved that the path graph Pn with n vertex and n -1edge is odd graceful, andthe cycle graph Cm with m vertex and m edges is odd graceful if and only if m even, she proved thecycle graph is not graceful if m odd. In this paper, firstly, we studied the graph m n C ¨¨P when m = 4, 6,8,10and then we proved that the graph m n C ¨¨P is odd graceful if m is even. Finally, we described analgorithm to label the vertices and the edges of the vertex set ( ) V Cm¨¨Pn and the edge set ( ) E Cm¨¨Pn .
%K Vertex labeling
%K edge labeling
%K odd graceful
%K Algorithms
%U http://airccse.org/journal/graphhoc/papers/0310jgraph8.pdf